Quiz de révision : Mathématiques Bac — Notions clés

Question 1 sur 10 10:00

[{"id":49991,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 1) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49992,"question":"La fonction f(x) = x³ - 3x est dérivable sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x³ - 3x est un polynôme, donc elle est dérivable sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49993,"question":"Quel est le domaine de définition de la fonction f(x) = √(4 - x²) ?","option_a":"A. [-2, 2]","option_b":"B. ]-∞, -2] ∪ [2, +∞[","option_c":"C. ℝ","option_d":"D. [0, 2]","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction √(4 - x²) est définie lorsque 4 - x² ≥ 0, soit x² ≤ 4, donc x ∈ [-2, 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49994,"question":"Soit une suite géométrique de raison q = 2 et de premier terme u₀ = 3. Quelle est la valeur de u₃ ?","option_a":"A. 6","option_b":"B. 12","option_c":"C. 24","option_d":"D. 48","option_e":"","option_f":"","bonne_reponse":"C","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 3 × 2³ = 3 × 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49995,"question":"La fonction exponentielle f(x) = eˣ est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle eˣ est strictement positive pour tout x ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49996,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² + 2x en x = 1 ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 4","option_d":"D. 6","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le coefficient directeur de la tangente est donné par f'(x). f'(x) = 2x + 2, donc f'(1) = 2×1 + 2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49997,"question":"Soit une variable aléatoire X suivant une loi normale N(0, 1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"A. 0.6826","option_b":"B. 0.8413","option_c":"C. 0.9772","option_d":"D. 0.9987","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite N(0, 1), P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49998,"question":"La fonction f(x) = ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49999,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ceˣ","option_b":"B. y = Ce⁻²ˣ","option_c":"C. y = C + eˣ","option_d":"D. y = Cx","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce⁻²ˣ, où C est une constante réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50000,"question":"Soit un triangle ABC rectangle en A. Si AB = 3 et AC = 4, quelle est la longueur de l'hypoténuse BC ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]